MHD INSTABILITIES IN SHEAR FLOWS OF ANISOTROPIC COSMIC PLASMAS. I. FIRE HOSE MODES

Abstract

The stability of the anisotropic collisionless plasma layer to small disturbances in the MHD description is studied based on moment equations obtained from the Vlasov kinetic equation taking into account the heat flow along the spatially shearing flow. To find the complex spectral parameter that determines the growth rate of instability, on the base of the obtained wave equation, the boundary value problem is solved using WKB approximation for the case of a smooth hyperbolic velocity profile. A general integral dispersion equation, based on these solutions is obtained. This equation describes all types of body and interface instabilities in the presence of heat flow along the magnetic field, well studied for infinite stationary and homogeneous anisotropic plasma. It is shown that reducing the layer width greatly enhances the mirror instability, and strongly suppresses the oblique fire-hose instability. We limited ourselves here to study how the spatial gradient of the plasma flow affects the properties of an aperiodical oblique fire-hose instability in a limited layer. It was found that the spatial gradient in flow velocity greatly enhances this instability. With a narrowing of the shearing layer width and an increasing of the velocity gradient, the body hose modes transform into surface Kelvin-Helmholtz modes existing on the interface between the two parts of the flow with the different velocities